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Submission #966342

# Submission time Handle Problem Language Result Execution time Memory
966342 2024-04-19T17:50:15 Z MisterReaper Split the sequence (APIO14_sequence) C++17
71 / 100
 2000 ms 80884 KB 
#include <bits/stdc++.h>

using i64 = long long;

struct line {
    i64 a, b;
    line(i64 _a, i64 _b) : a(_a), b(_b) {}
    long double intersect(line rhs) {
        return (long double)(b - rhs.b) / (rhs.a - a);
    }
    i64 eval(i64 x) {
        return a * x + b;
    }
    bool operator== (line rhs) {
        return a == rhs.a && b == rhs.b;
    }
};
long double intersect(line a, line b, line c) {
    return (a.b - b.b) * (c.a - b.a) >= (b.b - c.b) * (b.a - a.a);
}
namespace std {
    std::string to_string(line l) {
        return '(' + to_string(l.a) + "x + " + to_string(l.b) + ')';
    }
};

#ifdef DEBUG 
    #include "debug.h"
#else
    #define debug(...) void(23)
#endif

constexpr int maxN = 1E5 + 5;
constexpr int maxK = 200 + 5;

int A[maxN], go[maxK][maxN];
i64 p[maxN];

signed main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);

    int N, K;
    std::cin >> N >> K;

    for(int i = 1; i <= N; i++) {
        std::cin >> A[i];
    }

    for(int i = 1; i <= N; i++) {
        p[i] = p[i - 1] + A[i];
    }

    std::deque<std::pair<line, int>> dq;
    auto size = [&]() -> int { return (int) dq.size(); };
    auto Add = [&](line l, int idx) -> void {
        while(size() >= 2 && (l == dq[0].first || intersect(l, dq[0].first, dq[1].first))) {
            dq.pop_front();
        }
        if(size() && l == dq[0].first) {
            dq.pop_front();
        }
        dq.emplace_front(l, idx);
    };
    auto Query = [&](i64 x) -> std::pair<i64, int> {
        int l = 0, r = size() - 1;
        while(r - l > 3) {
            int m = (l + r) >> 1;
            if(dq[m].first.eval(x) < dq[m + 1].first.eval(x)) {
                l = m + 1;
            } else {
                r = m;
            }
        }
        auto ans = std::pair{dq[l].first.eval(x), dq[l].second};
        for(int i = l; i <= r; i++) {
            ans = std::max(ans, std::pair{dq[i].first.eval(x), dq[i].second});
        }
        return ans;
    };

    std::vector<i64> dp(N + 1);
    for(int k = 1; k <= K; k++) {
        dq.clear();
        Add({0, 0}, 0);
        std::vector<i64> ndp(N + 1);
        for(int i = 1; i <= N; i++) {
            // for(int j = 0; j < i; j++) {
            //     if(dp[k - 1][j] + 1LL * (p[i] - p[j]) * (p[N] - p[i]) >= dp[k][i]) {
            //         go[k][i] = j;
            //         dp[k][i] = dp[k - 1][j] + 1LL * (p[i] - p[j]) * (p[N] - p[i]);
            //     }
            // }

            auto [v, j] = Query(p[N] - p[i]);
            ndp[i] = v + 1LL * p[i] * (p[N] - p[i]);
            go[k][i] = j;
            Add(line{-p[i], dp[i]}, i);
            debug(dq);

            debug(k, i, ndp[i], go[k][i]);
        }
        dp = std::move(ndp);
    }

    int ans = 1;
    for(int i = 1; i < N; i++) {
        if(dp[i] >= dp[ans]) {
            ans = i;
        }
    }

    std::cout << dp[ans] << '\n';

    std::vector<int> v;
    for(int k = K; k >= 1; k--) {
        v.emplace_back(ans);
        ans = go[k][ans];
    }

    for(int i = K - 1; i >= 0; i--) {
        std::cout << v[i] << " \n"[i == 0];
    }

    return 0;
}

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2392 KB contestant found the optimal answer: 108 == 108
2 Correct 1 ms 2396 KB contestant found the optimal answer: 999 == 999
3 Correct 1 ms 2396 KB contestant found the optimal answer: 0 == 0
4 Correct 1 ms 4452 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 1 ms 6492 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 0 ms 2396 KB contestant found the optimal answer: 1 == 1
7 Correct 0 ms 2392 KB contestant found the optimal answer: 1 == 1
8 Correct 1 ms 2396 KB contestant found the optimal answer: 1 == 1
9 Correct 1 ms 2396 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 1 ms 2396 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 1 ms 2396 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 1 ms 4444 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 1 ms 4440 KB contestant found the optimal answer: 140072 == 140072
14 Correct 1 ms 2392 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 1 ms 4444 KB contestant found the optimal answer: 805 == 805
16 Correct 1 ms 2396 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 1 ms 4444 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2396 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 1 ms 2396 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 3 ms 20828 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 2396 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 1 ms 6492 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 1 ms 4440 KB contestant found the optimal answer: 933702 == 933702
7 Correct 2 ms 12708 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 1 ms 6492 KB contestant found the optimal answer: 687136 == 687136
9 Correct 1 ms 4444 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 1 ms 6488 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2392 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 2396 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 27 ms 80476 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 2396 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 9 ms 57692 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 16 ms 72280 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 24 ms 80472 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 3 ms 18780 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 2 ms 12636 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 4 ms 23036 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2396 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 2392 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 40 ms 80520 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 2648 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 32 ms 80504 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 27 ms 68184 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 34 ms 80424 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 31 ms 80492 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 8 ms 16728 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 14 ms 33308 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 2908 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 5 ms 2908 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 309 ms 80884 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 5 ms 3092 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 194 ms 50112 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 216 ms 58308 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 240 ms 60428 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 206 ms 50184 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 230 ms 58316 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 286 ms 72692 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 48 ms 8496 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 48 ms 8444 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Execution timed out 2013 ms 48100 KB Time limit exceeded
4 Halted 0 ms 0 KB -